Criminal prosecutions may be out of the question, but demotions and dismissals are not.

If none are forthcoming, we’re not sure why anybody should put much faith in the professionalism and integrity of the Chicago Police Department.

In a report released Tuesday, special prosecutor Dan K. Webb depicts a Police Department that completely botched — or willfully derailed — two separate investigations into the 2004 death of 21-year-old David Koschman.

The first investigation, in 2004, was a joke — police work at its worst. It ended with no charges being filed against the man who punched Koschman, Richard J. Vanecko, a nephew of former Mayor Richard M. Daley. The cops either slow-walked the investigation or got their training at the Barney Fife Police Academy.

The second investigation, in 2011, was a twisted affair clearly intended to confirm the findings of the first investigation, no matter how the evidence had to be contorted, fabricated or ignored.

In both investigations, Webb’s report makes clear, the police and Cook County state’s attorney’s office essentially concocted a case of self-defense for Vanecko, even to the point of asserting his likely motives for punching Koschman, miraculously without even questioning him.

Webb found no evidence that Daley or anybody else pulled strings, which is really too bad. Because if there was no political conspiracy, then both Koschman investigations may simply be examples of routine Chicago Police incompetence — and that’s scary.

Consider the bad judgment behind CPD’s very first move in the 2004 investigation: a sergeant assigned the case to two detectives who were going on vacation or furlough in three days. The two detectives worked the case for one day, not three, then took their extended time off, and nobody bothered to reassign the case to other detectives. It just sat there.

Webb offers a priceless set piece of how Detective James Gilger, working with Detective Nicholas Spanos, skewed the facts in Vanecko’s favor in a 2011 report.

In the report, Gilger concludes that Koschman yelled “F— you! I’ll kick your ass!” moments before Vanecko punched him. Webb notes that no witness in any police report said that Koschman said this.

Gilger claims Koschman was “going after Vanecko” and “clearly the assailant.” This conclusion, Webb notes, is not supported by other police reports or even by Gilger or Spanos’ own notes.

Gilger concludes that Koschman’s actions “caused Vanecko to take action and defend himself.” Webb says that conclusion has no basis in anything said by a witness.

And then there were the facts, Webb says, that Gilger “either ignored or failed to consider.” The detective, for example, made no mention of the height and weight disparities between Vanecko (a big guy) and Koschman (a mouthy guy, but a little guy).

As we say, if there was no political conspiracy here, that’s not entirely reassuring. We would like to think the Chicago Police are more competent, when they’re trying, than this. But based on Webb’s report, it is reasonable to suspect there was at least a minimum of willful intent — if not a conspiracy — by some members of law enforcement to slow or misdirect the Koschman investigations. Nobody had to tell anybody that going after a Daley might not be a ticket to a promotion.

What else, one might ask, can explain the mysterious disappearance of four important police files in the Koschman case, the sudden re-emergence of those files and the fact that one detective, Lt. Denis P. Walsh, had “ties” — Webb’s word — to all four files?

Webb states that he considered filing charges against six current Chicago Police officers, including Walsh, Gilger and Spanos, but decided there was insufficient evidence to convict them.

But if the door has closed on criminal charges — and we are not saying it has — the Chicago Police Department and Cook County state’s attorney’s office still can take disciplinary action against the worst offenders identified by Webb.